1. Field of the Invention
The present invention relates to a delta-sigma modulator and in particular to a method and apparatus for calibrating a continuous-time delta-sigma modulator.
2. Description of the Related Art
Delta-sigma modulators are widely used in over-sampling analog-to-digital converters (ADC) to achieve high-resolution analog-to-digital data conversion despite using coarse quantization. To date, most delta-sigma modulators use discrete-time loop filters. There has been much interest lately to use continuous-time loop filters. FIG. 1 depicts a block diagram of a typical delta-sigma modulator 200 that employs a continuous-time loop filter. For example, a continuous-time (or analog) input signal x(t) is fed to a quantizer 240 via a continuous-time loop filter 230 and converted into a discrete-time output sequence y[n]. The output sequence y[n] is fed back via a digital-to-analog converter (DAC) 260 to the continuous-time loop filter 230 as a second input. The quantizer 240 converts an input continuous-time signal into discrete-time samples at a rate controlled by a clock. The continuous-time loop filter 230 is usually constructed using one or more continuous-time integrators which are designed to mimic an ideal response of 1/sT, where T corresponds to a period of the clock. The continuous-time loop filter 230 also involves one or more signal routing and summing. For instance, a third order continuous-time loop filter 230 using three continuous-time integrators and three summing operations is depicted in FIG. 2.
The modulator output sequence y[n] is determined by the continuous-time input signal x(t), quantization error due to the quantizer 240, and response of the continuous-time loop filter 230. Although an explicit sampling circuit does not exist in the modulator 200 to convert the continuous-time input signal x(t) into discrete-time samples x[n], there is an implicit sampling operation performed on x(t) due to the quantizer 240 that operates synchronously with the clock. In accordance with the clock, the quantizer 240 generates a discrete-time output sequence which is also the output sequence y[n] of the modulator 200.
Equivalence theorem states that the continuous-time input signal x(t) can be represented equivalently by the discrete-time samples x[n]=x(t=nT) as far as its effects to the discrete-time output sequence y[n] is concerned. Along this line of thinking, FIG. 3A depicts a behavioral model commonly used to model the continuous-time delta-sigma modulator 200. For example, a sampler 205 converts the continuous-time input signal x(t) into the discrete-time samples x[n]. The behavior of the quantizer 240 is modeled as adding a quantization error sequence q[n] into the system. The discrete-time samples x[n] are filtered by a discrete-time filter G(z) 241 while the quantization error sequence q[n] is added to an output of the discrete-time filter 241 via a summer 249 to generate the output sequence y[n]. The output sequence is filtered by a discrete-time filter L(z) 243 before being fed back to be subtracted from the output of the discrete-time filter 241 via a summer 247. By way of example, the responses of the discrete-time filters G(z) 241 and L(z) 243 corresponding to the modulator depicted in FIG. 2 are as follows:G(z)=(1+z−1)/2/(1−z−1)3; andL(z)=g1/(z−1)+g2/2·(z+1)/(z−1)2+g3/6·(z2+4z+1)/(z−1)3.
FIG. 3B depicts a simplified version of the behavioral model depicted in FIG. 3A. For example, a sequence of the discrete-time samples x[n] is filtered by a signal transfer function STF(z) 245 while the quantizer error sequence q[n] is filtered by a noise transfer function NTF(z) 255. An output of STF(z) 245 is summed with an output of NTF(z) 255 in a summer 265 to result in the modulator output sequence y[n]. Both STF(z) 245 and NTF(z) 255 are determined by the loop filter 230. The responses of STF(z) 245 and NTF(z) 255 are related to the responses of G(z) 241 and L(z) 243 via the following relations:STF(z)=G(z)/(1+L(z)); andNTF(z)=1/(1+L(z)).
Internal parameters of the continuous-time loop filter 230 (e.g., coefficients g1, g2, and g3 in the loop filter 230 shown in FIG. 2) are chosen to achieve a target noise transfer function. Usually, it is desirable to have a noise transfer function that strongly suppresses the quantization noise within a band of interest and thus improves an in-band signal-to-quantization-noise ratio. For example, a choice of g1=11/6, g2=2, and g3=1 would result in a classic third order noise transfer function of (1−z−1)3.
When implementing a modulator in an integrated circuit, the internal parameters of the loop filter 230 (e.g., the coefficients g1, g2, and g3 of the loop filter 230 shown in FIG. 2) are usually determined by ratios between resistors or capacitors. Modern integrated circuits usually provide good matching between values of circuit components of the same kind. Although for each individual resistor/capacitor the value may be off by as much as 30%, for example, the ratio between the values of two resistors/capacitors of the same kind is usually very accurate (e.g., accurate to within 0.1%). Therefore, the effective values of the coefficients g1, g2, and g3 usually can be controlled very well in an integrated circuit. The biggest problem usually arises from the inaccuracies within the integrators.
A continuous-time integrator is usually implemented either by an OTA-C integrator shown in FIG. 4A or an R-C integrator shown in FIG. 4B. For the OTA-C integrator, an input voltage is converted into an output current by an operational transconductance amplifier (OTA). The output current is then integrated by a capacitor and converted into an output voltage. The voltage transfer function of the OTA-C integrator is Gm/sC, which matches the desired response of 1/sT if the transconductance Gm and capacitor C are properly chosen such that T=C/Gm, i.e., the “time constant” C/Gm is equal to the clock period. For the R-C integrator, due to the high gain of the operational amplifier, the transfer function for the input voltage to the output voltage is 1/sRC, which matches the desired response of 1/sT if the values of resistor R and capacitor C are properly chosen such that T=RC, i.e., the “time constant” RC is equal to the clock period. However, in practice, there is always spread in component values in a real circuit. For example, in a typical complementary metal oxide semiconductor (CMOS) integrated circuit, the uncertainty in the transconductance, resistor, and capacitor values may cause the value of C/Gm or RC of an integrator to deviate from its design value by up to 30%. This usually causes performance degradation to the modulator. Worse yet, it may result in instability and cause the system to fail. In addition, both C/Gm and RC are temperature dependent. Therefore, even if the value of C/Gm or RC is calibrated at start-up, it may deviate from the initial value as the temperature drifts.